An apparatus has been known which diagnoses a breast cancer by transmitting ultrasound that is elastic waves, receives waves reflected by an internal part of a subject and acquires an ultrasonic echo image. PTL 1 discloses a method which mechanically scanning a probe having elements that exchange ultrasound one-dimensionally and generates three-dimensional image data.
On the other hand, adaptive signal processing has been developed in a radar field, for example. Constrained Minimization of Power (CMP) which is one method of adaptive signal processing which minimizes the signal power when radio waves are received with a plurality of elements by fixing the sensitivity for one direction. According to the adaptive signal processing, the processing parameter is adaptively changed direction by direction. This kind of adaptive signal processing method advantageously may improve the spatial resolution, particularly, the resolution in orientation direction. NPL 1 discloses a method which uses such an adaptive signal processing method to generate ultrasonic echo image data for a higher resolution.
Processing to be performed when adaptive signal processing is applied to an ultrasonic received signal will be described on the basis of CMP, for example. First of all, the processing will be described up to calculation of a correlation matrix from a received signal. Hilbert transform, that is, delay processing circuit according to a target position is first performed on received signals output from a plurality of elements. A complex-represented received signal is thus acquired. When the sth sample of signals acquired by processing a received signal from the kth element is xk[s], the input vector X[s] of the sth sample may be defined as:X[s]=[x1[s],x2[s], . . . ,xM[s]]T  [Math.1]where M is the number of elements.
The input vector X[s] is used to calculate a correlation matrix Rxx.
                                                                        R                xx                            =                            ⁢                              E                ⁡                                  [                                                            X                      ⁡                                              [                        s                        ]                                                              ⁢                                                                  X                        H                                            ⁡                                              [                        s                        ]                                                                              ]                                                                                                        =                            ⁢                              [                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                1                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                                                        E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                2                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                                ⋮                                                              ⋮                                                              ⋱                                                              ⋮                                                                                                                          E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                1                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                                    E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                2                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                            …                                                                                      E                        ⁡                                                  [                                                                                                                    x                                M                                                            ⁡                                                              [                                s                                ]                                                                                      ⁢                                                                                          x                                M                                *                                                            ⁡                                                              [                                s                                ]                                                                                                              ]                                                                                                                    ]                                                                        [                  Math          ⁢          .2                ]            
The “H” at the right shoulder in the expression indicates a complex conjugate transposition, and “*” at the right shoulder indicates a complex conjugate. E[ ] expresses processing of calculating a time average and means that the sample number (“s” here) is changed to calculate the average.
Next, in order to prevent the influence by correlated interference waves that reach from a position excluding a target position to a probe, a space average method is applied to the correlation matrix Rxx to acquire the average correlation matrix R′xx.
                              R          xx          ′                =                              ∑                          n              =              1                                      M              -              K              +              1                                ⁢                                          ⁢                                    z              n                        ⁢                          R              xx              n                                                          [                  Math          ⁢          .3                ]            
Rnxx indicates a submatrix of the correlation matrix Rxx and moves on a diagonal component of Rxx. Rnxx has a K*K size with the (n,n) component of Rxx as the first diagonal component. Zn is a coefficient for calculating a submatrix and is adjusted such that the total sum of Zn may be equal to 1.
According to CMP, a weight for minimizing the output power under a constrained condition is acquired. The weight is a weight represented by a complex vector. When the sensitivity against an ultrasonic received signal from a target position is constrained to 1, the optimum weight Wopt for minimizing the output power may be acquired in CMP by the following expression.
                                          W            opt                    =                                    γR              xx                              ′                -                1                                      ⁢            C                          ,                                  ⁢                  γ          =                      1                                          C                H                            ⁢                              R                xx                                  ′                  -                  1                                            ⁢              C                                                          [                  Math          ⁢          .4                ]            
C is a constrained vector and changes in accordance with the position of an element and a target position. However, when delay processing circuit is performed on received signals, all values of C may be 1 in the size (K in this case) of the average correlation matrix. The power Pmin calculated by using the weight Wopt may be acquired as follows:
                              P          min                =                              1            2                    ⁢                      1                                          C                H                            ⁢                              R                xx                                  ′                  -                  1                                            ⁢              C                                                          [                  Math          ⁢          .5                ]            
In this way, according to CMP, a correlation matrix and even an average correlation matrix are acquired from received signals. The inverse matrix may be used to calculate a weight or the power when a weight is used. The weight or the power when a weight is used is a weight or power when the sensitivity from a target position against an ultrasonic signal is defined to 1 to suppress ultrasonic signals from other positions. In other words, CMP allows selective extraction of an ultrasonic signal from a target position, resulting in a higher spatial resolution. Notably, the power may be calculated by QR decomposition and back substitution processing, instead of direct calculation of the inverse matrix.